  
  
Stat 
Members: 2708 Articles: 1'972'659 Articles rated: 2572
16 July 2020 

   

Article overview
 

Combinatorial congruences modulo prime powers  ZhiWei Sun
; Donald M. Davis
;  Date: 
4 Aug 2005  Subject:  Number Theory; Combinatorics MSCclass: 11B65; 05A10; 11A07; 11B68; 11S05  math.NT math.CO  Abstract:  Let $p$ be any prime, and let $a$ and $n$ be nonnegative integers. Let $rin Z$ and $f(x)in Z[x]$. We establish the congruence $$p^{deg f}sum_{k=r(mod p^a)}inom{n}{k}(1)^k f((kr)/p^a) =0 (mod p^{sum_{i=a}^{infty}[n/{p^i}]})$$ (motivated by a conjecture arising from algebraic topology), and obtain the following vast generalization of Lucas’ theorem: If $a>1$ and $l,s,t$ are nonnegative integers with $s,t  Source:  arXiv, math.NT/0508087  Services:  Forum  Review  PDF  Favorites 


No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser CCBot/2.0 (https://commoncrawl.org/faq/)

 



 News, job offers and information for researchers and scientists:
 